The Observant Astronomer

The passing scene as observed by an observant Jew, who daylights as an astronomer.

Friday, March 10, 2006

The Number of Stars in the Universe

A reader asks
What can you tell me about chazal's take on the number of stars and what modern science says today and are the numbers the same and whether you feel that this is a proof of torah shbaal peh?

The relevant text is Gamara Brachos 32b:
אמר לה הקב"ה בתי י"ב מזלות בראתי ברקיע ועל כל מזל ומזל בראתי לו שלשים חיל ועל כל חיל וחיל בראתי לו שלשים לגיון ועל כל לגיון ולגיון בראתי לו שלשים רהטון ועל כל רהטון ורהטון בראתי לו שלשים קרטון ועל כל קרטון וקרטון בראתי לו שלשים גסטרא ועל כל גסטרא וגסטרא תליתי בו שלש מאות וששים וחמשה אלפי רבוא כוכבים כנגד ימות החמה
where Reish Lakish quotes Hashem as saying he created 12 constellations, for each constellation 30 chiel, for each chiel, 30 ligyon, for each ligyon, 30 rehaton, for each rehaton, 30 karton, for each karton, 30 gistera, and for each gistera, 365 thousand myriad stars. Multiply it out and you've got 12 x 305 x 365 x 1,000 x 10,000 or about 1018 stars. An impressively large number, indeed.

So what does "science" have to say about this question? In context, we must be asking how many stars are there in the observable universe. This, at least, is finite, since the further away we look the further back in time we look and the universe has a finite age according to current understanding. Stars are found in galaxies, so, to estimate the number of stars in the universe we need to worry about three factors: The typical number of stars in a typical galaxy, the number of such galaxies in a typical volume of space (the galaxy density), and the total volume containing galaxies.

The most recent such estimate for the number of visible stars in the universe is that of Prof. Simon Driver, presented at the 2003 General Assembly of the International Astronomical Union. He comes up with 7 x 1022 stars. And this is probably a lower limit since he's only counting stars within the reach of his telescope.

Well, he doesn't really count the stars. What he's done is count the number of galaxies within a (relatively large) strip of sky and estimated how many stars are in those galaxies from their brightnesses. Then he's multiplied that number by the total number of such strips needed to cover the whole sky. Or at least that's what I assume he's done based on the article. Nothing has been published regarding the calculation.

My correspondent quotes some old mail-Jewish discussions on the subject.
The number itself is amazing (10^18). This is (cosmically speaking) pretty darn close to the current estimate of 10^22.

gemara (Brachot 32b) _does_ count the number of stars in the sky, or at least calculates the number, and comes up with 12*(30^5)*364*(10^7) = 1.0512 * 10^18. On a logarithmic scale, this is surprisingly close to the best modern astronomical estimate, which is about 10^21.

How accurate is Prof. Driver's number? Without knowing how he does it, I couldn't say. Given the sort of assumptions he's likely making I would be surprised if he's off by more than a factor of 100 or so in either direction, though. Which is important, because his number is 70,000 times larger than that of R"L. Those who would like to claim that the two numbers are equivalent are guilt of innumeracy. Just because two numbers are large, doesn't mean that they are the same, and a factor of 70,000 is far too large to brush under the table. Let me illustrate what this factor means. Pick a stretch 6 km long on your favourite highway. The Moon is 70,000 times further away. Can you actually claim that bit of highway is as far as the Moon?

Some attempts to deal with the numbers:
What I cannot figure out is which assumptions the astronomers are making that could be tweaked in order to make the numbers match better. The simplest would be to lower the number of stars in an average galaxy to 10^4. But that seems awfully small. Any thoughts?

By the way the wording of the passage is curious Reish Lakish doesn't have the vocabulary to state such a big number so he talks in terms of what we would call galaxies and galactic clusters.

Avg galaxy ("gastara") = about 4x10^9 stars
Avg local cluster ("karton") = 30 galaxies
Avg supercluster ("rahaton") = 30 clusters

It goes on to say that superclusters are grouped into clusters of about 30 (megasuperclusters?) and that these are in turn grouped into an even bigger pattern of about 30 (hypermegasuperclusters?) of which the universe has a total of (about) 365.

Moreover from my amateurish research it seems that one of the prevailing theories of cosmic structure is that it is fractal and is not the calculation of Berachot 32a an example of fractal structure (4billionx30x30x30x30x360)?

Is this a "proof" of Torah sh'bal-peh? I wouldn't say so, and I think it a mistake to argue so. From one perspective, R"L would need another three layers of factors of 30 to be in the same ballpark, but his way of calculating the number of stars has nothing to do with the way they are really distributed in the universe. All those groups of 30s correspond to nothing observed, and resorting to "fractal geometry" and "hypermegasuperclusters" doesn't make it any better.

From another perspective, who is to say that the Prof. Diver's number is correct? Let any of his assumptions be wrong, and that number could increase, or decrease, possibly significantly. I think it presumptuous to assume that as of today science has "the correct answer" which can be used to validate Torah.

Besides, the whole argument misses, I think, the point of that gemara. The context is that Knesset Israel is complaining to HaKodsh Baruch Hu (i.e. G-d) that she has been forgotten by him. R"L has Hashem answer that he's created an incredibly unimaginable number of stars, every last one of which are for the sake of the Jewish people; how can she say he's forsaken her? In that context, is the number really intended to be precise? One can read it, instead, as a deliberate hyperbole, with no intention that the actual number be taken seriously. What is much more interesting, perhaps, is that R"L is willing to suggest that there are vastly more stars than those that are visible to the naked eye. If you want to hang something on this gemara, I think that that is a somewhat more fruitful direction than innumerate and presumptuous comparisons of very large numbers of dubious precision.


Blogger Rebeljew said...

"The simplest would be to lower the number of stars in an average galaxy to 10^4. But that seems awfully small. Any thoughts?"

The commenter proposes that there are 10,000 stars in an average galaxy. Um, I think we can safely ditch that one.

But I disagree that that RL was speaking of more stars than he could observe. I would further propose the radical idea that RL had no idea about galaxies, clusters, or even a concept that some stars were significantly farther away than others. He looked at points of light without any precision, based on his (perhaps fuzzy) eyesight. He saw different stars at different times of the year and he saw the Milky Way. Then he concluded, as you imply, that there were 18 gazillion jillion stars out there. He didn't COUNT them! He did not even estimate it. It would have nothing to do with his point!

So amateur psychologist wants to know why commenter wants a proof for TSBP from this gemora, and he what kind of acrobatics he is willing to perform to get a number that is plausible, even in orders of magnitude.

2:41 p.m., March 13, 2006  
Blogger The Observer said...

Oh, I never said he counted them, and he certainly had no idea about galaxies etc., but I doubt the Milky Way helped him much either. To the naked eye, it is just a fuzzy patch and discovering it could be resolved into stars was one of the things that had to wait for Galileo's telescope. There are of order 10^4 naked eye stars. Even if you were to estimate the number of stars in the Milky Way, you still wouldn't get a number 14 orders of magnitude larger.

I replied to the question in much the way I posted this here, and he shelved the issue.

11:43 a.m., March 15, 2006  

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